The Outward Radial Offset of Neptune Ring Arcs

Abstract

The designation of the customary restricted three-body disturbing potential $Φ$ as the perturbation Hamiltonian is believed to be the cause of Neptune ring arcs' radial offset between theories and observations. To identify the appropriate perturbation Hamiltonian, the energy integral in the fixed frame of a restricted three-body system, consisting of the central, primary, and test bodies, is reconsidered. It is shown that the perturbation energy includes the disturbing potential $Φ$ and the potential arising from the angular momentum terms of the test body. Both potentials happen to be singular as the test body goes to infinity contradicting to the perturbation nature. These two potentials can be combined to an energy relevant disturbing potential $Φ^{*}=βΦ$ which is regular at infinity because of the cancellation of the singularities. For circular orbits of the primary, the energy equation is conservative, and $Φ^{*}$ is identified as the perturbation Hamiltonian. Applying this result to evaluate the backgrund effect of Triton to the arc-Galatea system of Neptune, it is shown that there is a small difference $ΔΦ=(Φ^{*}-Φ)$ which amounts to an outward radial offset of the corotation location of Galatea by 0.3 Km. The mismatch between the pattern speed of Galatea's corotation potential and the mean motion velocity of the arcs could be resolved by considering the finite mass of Fraternite. However, by using $Φ^{*}$, Galatea's eccentricity could be reassessed in terms of the mass of Fraternite.